Cramér asymptotics for finite time first passage probabilities of general Lévy processes
We derive the exact asymptotics of P(supu<=tX(u)>x) if x and t tend to infinity with x/t constant, for a general Lévy process X that admits exponential moments. The proof is based on a renewal argument and a two-dimensional renewal theorem of Höglund [Höglund, T., 1990. An asymptotic expression for the probability of ruin within finite time. Ann. Prob., 18, 378-389].
Year of publication: |
2009
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Authors: | Palmowski, Zbigniew ; Pistorius, Martijn |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 79.2009, 16, p. 1752-1758
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Publisher: |
Elsevier |
Saved in:
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